Question: Khan.scratchpad.disable(); To move up to the maestro level in her piano school, Vanessa needs to master at least $105$ songs. Vanessa has already mastered $24$ songs. If Vanessa can master $2$ songs per month, what is the minimum number of months it will take her to move to the maestro level?
Solution: To solve this, let's set up an expression to show how many songs Vanessa will have mastered after each month. Number of songs mastered $=$ $ $ Months at school $\times$ Songs mastered per month $+$ Songs already mastered Since Vanessa Needs to have at least $105$ songs mastered to move to maestro level, we can set up an inequality to find the number of months needed. Number of songs mastered $\geq 105$ Months at school $\times$ Songs mastered per month $ +$ Songs already mastered $\geq 105$ We are solving for the months spent at school, so let the number of months be represented by the variable $x$ We can now plug in: $x \cdot 2 + 24 \geq 105$ $ x \cdot 2 \geq 105 - 24 $ $ x \cdot 2 \geq 81 $ $x \geq \dfrac{81}{2} \approx 40.50$ Since we only care about whole months that Vanessa has spent working, we round $40.50$ up to $41$ Vanessa must work for at least 41 months.